If f(x)=x^4+ax^3+bx^2+cx+d such that f(1)=f(2)=f
(3)=f(4), find the value of b.
Can anybody tell me the answer with proper
explanation?

• 
  ans b=35
  
  f(1)=1+a+b+c+d
  f(2)=16+8a+4b+2c+d
  f(3)=81+27a+9b+3c+d
  f(4)=256+64a+16b+4c+d
  
  given
  
  f(1)=f(2)=f(3)=f(4)
  
  firstly
  
  f(1)=f(2)
  1+a+b+c+d=16+8a+4b+2c+d
  7a+3b+c=-15...........................................................equ(1)
  
  then
  f(1)=f(3)
  we get
  13a+4b+c=-40...........................................................equ(2)
  
  then
  f(1)=f(4)
  we get
  21a+5b+c=-85..........................................................equ(3)
  
  
  solve equ(2)-equ(1)
  we get
  6a+b=-25......................................equ(4)
  
  solve equ(3)-equ(2)
  we get
  8a+b=-45......................................equ(5)
  
  solve equ(4) and equ(5) and put the value in other equactions for all the values
  we get
  a=-10 ,b=35,c=-50
  
  
  proof
  
  put the value of a ,b,c
  we get
  f(1)=f(2)=f(3)=f(4)
  
  
  
  
  
• 9 years agoHelpfull: Yes(45) No(1)
• i ansrwed it can't be determined in exam
• 9 years agoHelpfull: Yes(2) No(2)